ESCAPE FROM L.A.: The Rangers signed former Kings left wing Alexander Frolov to a cap-friendly, one-year, $3 million contract. Photo: Getty Images

The Rangers upgraded their offensive capabilities yesterday by signing left wing Alexander Frolov to a one-year, $3 million deal that is not only cap-friendly but should serve as motivation for a player looking to build leverage in the market.

There is nothing negative about the signing of the 28-year-old winger whose personally disappointing 51-point season (19-32) in Los Angeles would have made him the Rangers’ third-leading scorer and whose contract leaves general manager Glen Sather enough cap space with which to maneuver.

The Blueshirts currently have approximately $6.7 million of space under the summer cap with which to sign restricted free agent Marc Staal and perhaps another defenseman.

When defenseman Wade Redden is waived during camp and other summer charges are dropped at the end of September, the Blueshirts should go into the season with between $6.5-8 million of cap space, assuming Staal is in for between $4.5-5 million and depending on the final roster and the disposition of Donald Brashear’s $1.4 million, over-35 charge.

No, Frolov is not the elite center the club is thirsting for, but he has more immediate upside as a first-line bookend across from Marian Gaborik than either Brandon Dubinsky or Vinny Prospal, who were the two leading contenders for the job before the signing.

And yes, his addition muddies the depth chart for the team with a boatload of interchangeable forwards who don’t seem quite congruent, but it will fall on head coach John Tortorella and his staff to take the ingredients and mix them in a functioning recipe.

“I’ve told our guys that training camp will be a competition where they all will get the opportunity to earn the best spots available,” Tortorella told The Post by phone. “You know where Gabby is going to be, and I’ve scribbled down dozens of potential line combinations since we made this signing, but no one is going to be given an assignment or be eliminated from an assignment because of past history.

“I think Frolov makes us a more formidable team. I like him on the power play. I think we’ll certainly take a look at him with Gabby, but nothing is set. I don’t want to lock myself into anything in July. I don’t want to lock myself into anything in September.

“We didn’t make the playoffs last year. That should be explanation enough for why there are jobs and roles to be won. Guys will have to earn their ice time and their spot in the lineup no matter who they are.

“Plus, nobody should make the mistake of thinking that we’re closing off opportunities for the kids,” Tortorella said. “They’re going to get their chance.”

Frolov is strong on the puck, works the boards well and never has been reluctant to go to the dirty areas of the ice. He can shoot the puck, too.

“I would say for certain I am coming to New York with something to prove,” said Frolov, who scored 35 goals for the Kings in 2006-07 and 32 in 2008-09 but was relegated to center Michal Handzus’ checking line by coach Terry Murray most of last season. “I’ve been in the league [seven years] and know what I can do.

“I win battles, I can score goals on my shot and from around the net. I can see the play and I can pass. I’m very excited about this opportunity.”

Frolov rejected an offer from the Russian KHL believed to be for four years at between $18-20 million. He took the one-year offer — which Sather stood by — in order to re-establish his value.

“It was a very tough decision for me not to take the offer from Russia, but I wanted to stay in the NHL,” he said. “I signed for one year so I can improve and show everybody what I’m capable of.”